Let be a partition of sample space . If is any event, what is the formula for given by the Theorem on Total Probability?

Answer and explanation

Correct answer: B.

  1. Step 1: Because partition the sample space, the intersections are mutually disjoint and their union is .
  2. Step 2: .
Answer
.
Why not the others: Adding probabilities violates multiplication law; multiplying across terms confuses unions with intersections; and dividing ratios is mathematically invalid.

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